In a deep, medium-size pot, heat about 3 inches of oil over medium heat until temperature reads 350°F on a thermometer.
Meanwhile, make the waffles. In a large mixing bowl, whisk together the flour, cornmeal, sugar, baking powder, jalapeno, salt and 1 cup of the grated cheese.
In a separate mixing bowl, beat the eggs, then whisk in the buttermilk and vegetable oil.
Incorporate the wet ingredients into the dry ingredients and mix just until combined.
Heat a waffle iron and spray with nonstick spray. Pour 1 1/2 cups of the batter into the waffle iron and cook until golden brown, about 5 minutes. (Follow the manufacturer's directions. You may need to adjust amount of batter based on your waffle iron.) Transfer the waffles to a wire rack set over a baking sheet and quarter. Repeat with the remaining batter.
Make the fried chicken: In a medium bowl, whisk together the flour, cornstarch, salt, pepper to combine. Pour the buttermilk into a shallow baking dish.
Toss the chicken pieces in the flour mixture to coat.
Working in batches, dip the floured chicken into the buttermilk, then return it to the flour and toss to coat. Working in batches, add the breaded chicken to the hot frying oil. Don't crowd the pot with chicken, as it will bring down the temperature of the oil. Fry until golden brown and the chicken rises to the surface of the oil, 3 to 4 minutes. Remove the chicken from the oil and drain on a paper towel lined plate.
Just before serving, turn the broiler to low. Scatter the remaining 1 cup grated cheese over the waffles and broil just until the cheese has melted, about 1 minute. Let cool slightly, then place a piece of chicken on top of a waffle square and secure with a toothpick.